How do you derive rectangular core width and height from area and aspect ratio?
From PDVerse PnR Interview Handbook, part of the pdVerse Mentor Guide
Last updated:
Short Answer
This is one of the most basic but most-used floorplanning calculations — you know how much area your logic needs, and you've decided (for I/O, package, or routing reasons) what shape you want that area to take, and you need actual width/height numbers to build a floorplan from. 5 means twice as tall as wide.
Technical Explanation
- 5 means twice as tall as wide.
- Given total area
Aand your chosenAR, the two formulas fall right out of substitutingwidth = AR × heightintoA = width × height: - width = √(A × AR)
- height = √(A / AR)
- Sanity check with AR = 1 (a square): both formulas reduce to
width = height = √A— exactly what you'd expect, since a square with area A has side length √A. - Worked example: for A = 1,000,000 µm² and AR = 1 (square), width = √(1,000,000 × 1) = 1000 µm, and height = √(1,000,000 / 1) = 1000 µm — matching the reference example in the original answer.
- Keep your units consistent through every step (µm² for area, µm for dimensions) — mixing units here is a classic source of "why is my die 1000x too big" bugs.
- Don't stop at the raw math — after computing width/height, round to something that respects the manufacturing grid and lands on a legal row boundary (a whole number of standard-cell rows). A mathematically "correct" but non-grid-aligned dimension will just get silently snapped by the tool anyway, so it's better to round deliberately.
Visual Verification
Core Width = sqrt(Area / AR) and Core Height = sqrt(Area * AR). Calculated dimensions must snap to integer multiples of standard-cell row heights and site pitches.
Formula Or Decision Rule
Width [um] = sqrt(A [um^2] x AR); height [um] = sqrt(A [um^2] / AR).
What To Check
- Warning sign: Rounded dimensions change area or land off the manufacturing, site, or block grid.
- Inspect: choose one affected region, macro, row, pin, path, or net and trace the physical cause.
- Correct: Snap deliberately, recompute actual area and utilisation, and record the rounded values.
Command Checks & Actions
report_design-floorplan: reports the floorplan state understood by the tool
Run only the commands needed for this question. Save the report with the floorplan version and analysis context.
Healthy, Suspicious & Hard-stop Results
- Healthy: For area A and aspect ratio AR = width/height, width is sqrt(A x AR) and height is sqrt(A / AR). Keep units through every step.
- Hard stop: required legality or physical feasibility is missing or unexplained.
Common Mistake
The Trap: Do not hide the symptom with an arbitrary utilisation, halo, channel, blockage, pin move, or die-size change.
What The Interviewer Is Testing
” to measurable physical evidence and an owned correction.
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